Question

Let $O$ be the origin and $A$ be the point $(64, 0).$ If $P$, $Q$ divide $OA$ in the ratio $1 : 2 : 3$ , then the point $P$ is

• A. $\left(\frac{32}{3},0\right)$
• B. ( 32, 0 )
• C. $\left(\frac{64}{3},0\right)$
• D. ( 16, 0)

Answer 1

Answer: (A)

$\left(\frac{32}{3},0\right)$

Answer 2

Now, by internal section formula,

$P \equiv\left(\frac{1 \times 64+5 \times 0}{1+5}, \frac{1 \times 0+5 \times 0}{1+5}\right)$
$\equiv\left(\frac{64}{6}, 0\right)=\left(\frac{32}{3}, 0\right)$